Pages

Wednesday, January 28, 2015

We just had a fun, crazy and exhausting day for Super Science Saturday, a yearly K-12 outreach by our outstanding Regional Math and Science Center. The project had its start when my fellow traveler Heather Harrington sent me a picture of an awesome (and, later, prize winning) installation piece from Anila Quayyam Agha at ArtPrize. (Here’s a good article about the installation.) When I saw the the RMSC was focusing on light for Super Science Saturday the bulb went on.

Intersections, by Anila Quayyam Agha

How could that not inspire some excellent art and math?Our handout gave a little of the background, and some basic steps to cover.

People really gave it a go. Mostly the kids, although we did get a higher percentage of parents trying than expected. (Those who won't join in - what keeps them back? These are folks who are giving up a Saturday for their kid to do science, so...)Over and over we tried to emphasize:

We saw a lot of good mathematical and artistic problem solving. People measuring struts they'd need, considering options to construct, reverse engineering things they saw in other polytopes. They sought help when they were stuck, collaborated with neighbors and could verbalize what they were doing. They experimented with shadows, trying to figure out what angles of flashlight or position on the overhead showed the structure they wanted.It was difficult to get people to predict. The ones who did mostly found it more interesting to do the shadows and spent longer trying to match. For some reason, this was the highest level of parental involvement. The kids who were comparing shadows to a prediction drawing often had the parents jump in and want to see. Some people were interested enough in the connection with their predictions to trace the final

Some of what people seemed to learn about light and shadow is to start thinking of it as a projection from a single source, instead of a silhouette. People with right rectangular prisms or right pyramids were surprised at what you could see. Kids learned about the moving of shadows with the light source, and the effects of being closer or farther from the source.

Anna's gif experiment

Artistically people divided up between looking for symmetry, being representational (lots of houses) or crazy abstract. (My favorite to see, though when building I always go for symmetry.) There was a lot of pride of ownership - the vast majority of kids wanted to take their structure with them, and they were almost always excited to bring them back to show Heather, myself or a volunteer for the light work. Heather thought it was important for people to have a chance to enter into the art, to interact with the shadows, and that's why we did the overhead projector. It was a huge hit, and there was often a line of people waiting to see theirs on the big screen. Heather's other cool idea was to capture motion, as the changing shadows are visually interesting. We experimented with gif capture and Vines, but nothing was efficient enough to be able to handle hundreds of people.

2100 straws and 1000 pipe cleaners later, we were exhausted but energized.

We found the small aperture bar straws to be best, and picked up ours at Gordon Food Service, 500 to a box. About half a length was a good basic distance for the projector and flashlights - a whole 8" straw scale was too large. The flashlights were just $1 9 LED cheapos, but they were bright enough for strong shadows in an only half unlit room. The bulk pipe cleaner pack was the best deal, all the same color so as to avoid "I wants",cut into 5 or 6 pieces was enough to hold two straws together. If a pipe cleaner was loose in a straw, we'd hook the end of the pipe clearner to get a better grip. Originally I was going to cut the straws into Zome like proportions, but it was unnecessary as people mostly didn't make the classic solids. Flickr seemed to be the most efficient photosharing tool so that people could get the photos afterward. Take the picture from within the Flickr app, it uploads automatically, and you can set it to a public album with one touch.

People had the option to leave their sculpture and thank goodness some did because we recycled/cannibalized everything.

When people had the choice of tons of cool science activities, what kept us so busy? Some of those had lasers! I think it was the art aspect. In the other activities, though cool, you were doing what someone told you to do. What we had wasn't for everyone. The option to choose a premade sculpture was good to have (we had about 10 premade sculptures), as it allowed people to still engage in the shadow prediction and art.

Great day, good to collaborate with an artist, and a lot of creative mathematics. Who knows what mathematics dwells in the hearts of men?

PRINCIPLE ONE: Nonviolence is a way of life for courageous people. It is active nonviolent resistance to evil. It is aggressive spiritually, mentally and emotionally.

PRINCIPLE TWO: Nonviolence seeks to win friendship and understanding. The end result of nonviolence is redemption and reconciliation. The purpose of nonviolence is the creation of the Beloved Community.

PRINCIPLE THREE: Nonviolence seeks to defeat injustice not people. Nonviolence recognizes that evildoers are also victims and are not evil people. The nonviolent resister seeks to defeat evil not people.

PRINCIPLE FOUR: Nonviolence holds that suffering can educate and transform. Nonviolence accepts suffering without retaliation. Unearned suffering is redemptive and has tremendous educational and transforming possibilities.

PRINCIPLE FIVE: Nonviolence chooses love instead of hate. Nonviolence resists violence of the spirit as well as the body. Nonviolent love is spontaneous, unmotivated, unselfish and creative.

PRINCIPLE SIX: Nonviolence believes that the universe is on the side of justice. The nonviolent resister has deep faith that justice will eventually win.

I see these as connected to how I want to teach. My nonviolence training came from Sr. Liz Walters, IHM, when I was an undergrad at Michigan State. (Short bio of Liz from an award she received.) At that age, I was (so typically) filled with idea of competition and winning masquerading as justice. When I think back on the transition to peacefully campaigning for justice, and that the means matter as much or more than the ends, the training from Liz was of profound impact. Found this post with some current organizations that do nonviolence training.

So how is teaching related to these principles?

Active resistance to evil. Nonviolence is in no way nonaction. Instead, it is active pursuit of justice. Teaching is often inherently nonviolent because it is a career built on constructing relationships. Not that teaching automatically moves in this direction, because we can bring confrontational relationship strategies to the job. Most teachers are capable of careers that earn more or are essentially easier. Even teachers that leave the field I think have sometimes just finished what they had to give. Some vocations are for a season and some are for a lifetime. (When we lose the lifetime teachers because of school injustices, though, this is a serious loss. Personally and societally.)

Redemption may be strange language for education, but when we think about caring for all our students, it is going to include those wronged by the system or suffering from circumstance. When we work to create a safe learning space, it is naturally redemptive work. When we get to really know our students, it is constructive.

Defeat injustice, not people. This can be difficult, as students act out routines and responses to which which they have been subjected. But the classroom culture building to which I respond does an excellent job of separating the student from behavior.

How does suffering relate? One of the things I try to share with my preservice teachers is to be ready for this, what I often call the heartbreak of teaching. By caring for our students, we are volunteering to share their burdens. There are going to be students that have difficult, messy and painful lives, and we are signing up to walk part of the way with them. We are opposing the dehumanizing forces in our society that want to use them up or pass them over or sell their share for a profit.

Doesn't "spontaneous, unmotivated, unselfish and creative" describe a lot of the teachers you admire?

I also believe that teaching is inherently hopeful. We are siding with the universe on the side of justice, or our higher power, or whatever gives you faith.

So on this Martin Luther King, Jr. Day, I've taken some time to pray for teachers, pray for their students and pray for my students. I'm going to look for opportunities to stay in the struggle, and support those resisting injustice. And know that it isn't just for this day.

Friday, January 16, 2015

Preamble
Wow - I missed a blogging month. And I had so much to say about it... we did Math in Your Feet, some excellent student projects, lots of new lessons, assessment thoughts... So I was thinking about resolving to blog less big, more frequently. Then Sue Van Hattum blogs her #edustory, and I think challenges me and a few others...

I've been thinking about doing more microblogging - and maybe I'll try it. I get stopped by "nobody wants to read that" which makes me forget that I'm writing out my own understanding, so that shouldn't matter. I'm not an author who's trying to please a fan base, I'm a teacher trying to work my way to understanding.

Actual Post
But what's really on my mind is embodied cognition. Last summer I got to try a session with Malke Rosenfeld and Christopher Danielson at TMC14 on Embodied Cognition. (My account.) Outside of their session, Malke worked with Michael Pershan and Max Ray and others on doing a life size complex plane and number line. I wasn't even a part of that but it got me wondering. Malke and Max have continued to work on the idea, and there is an MTMS article in the works. They were willing to share their writing on that so I could try things in class.

The course is for preservice middle school teachers. I start off with negative numbers (and probably end with negative numbers too if you know what I mean. Where's my Dangerfield font?) because it is a good setting for talking about operations as story and action (exposing them to the CGI structures), and rolling in some content from our preservice elementary classes on fact families and operation strategies, models and landscapes of learning.

For the Cognitively Guided Instruction stories we watched the Kindergartener uses Direct Modeling video from the Heinemann site. Then sorted these stories. Usually students sort them by operation needed to solve them, but the video was a great focus, because they really did a great job discerning actions. The idea is that young students encountering stories before direct operation instruction classify stories by what's happening in them. Are amounts increasing or decreasing? Are we comparing separate amounts or looking at static groups of different types? They then model and invent strategies that fit the contexts. For example, students who are taught addition first but then have to use it in a decreasing context often have difficulty solving the story problems. (James gave away 3 pencils but still had 5 left. With how many did he start?)

We followed that by brainstorming contexts for negative numbers: money, debt, bills, weights/balloons, depth/sea level, golf, football yardage, temperature… the usual suspects but a good variety. When we tried writing stories for them, it was challenging to ask the questions in a way that the answer was negative. I nudged them towards the idea that one of the strongest contexts for negative numbers is when the numbers are describing change rather than direct quantities.

Some of the questions from Max and Malke:

where she was compared to where she started

tell us how far away from someone they were, and in what direction

a
plan for how everyone could, in a coordinated way, get from their home
position to their spot that was the same distance away but in the
opposite direction

identify if there was someone who was the same distance away from Shane, but in the opposite direction

give students a target result and ask them to come up with a series of moves that resulted in the given displacement

We just used stickies to make the numberline. I marked a square as 0 and asked the PSTs to place stickies for 5, 10, 15, -5, 10, -15. First discussion: are we using the squares or the edges in between? (Squares, because of placement of zero.)

Students moved to various numbers on the line, called out by the teacher. Discussion: left right, direction big part of idea of negative. Distance talk, however, is naturally positive.

Then we started
modeling change. If a student C walks from A to B: how far did they go? (Positive.) What is the change in their position? (Signed.) We did several iterations
of moving in both directions. Discussion: PSTs started noticing how zero figures into the strategies. Frequently found change by b to 0, 0 to c.

PSTs challenged in groups to come up with a question that could be modeled on the line.

1st
group: stood at 8, 5 and -3. Class brought up person at 8 could be
change: how big a change when walking from -3 to 5. Another said -3
could be how big a change from 8 to 5? Discussion: no way for 5 to be
the change in that situation.

Next
group of 2 stood at 14 and -7. Their story was: Samantha climbed a 14
foot hill and jumped in the water, sinking to 7 feet below the surface.
How far did she dive? Someone brought up 14, and dove 21 feet, where is
she? (“Dead”)

Shared
Max and Malke’s challenge to come up with a combination that resulted
in a net difference. Students proposed 3, 4 and 5 move challenges to get
the goal, took the challenge to mean literally standing on the line.
Brought up how the challenge could lead to better strategies than
counting one space at a time.

End of day 1, informal assessment: was this worth their time? All 4s and 5s on a 0 to 5 finger scale.

Day 2 we set the number line back up and started thinking about how to explicitly model addition and subtraction. The first group shared the idea to face positive: if addition of positive move forward, if subtraction of positive turn back, if negative turn... I raised my opposition to things that just feel like more rules and not connected to ideas. In discussion, the idea was raised to face neutral by default, turn positive to add and negative to sutract, walk forward for positive, walk backward for negative. I brought up how the class deciding this idea for themselves is probably the most valuable part.

Once we had decided on the representation, we got to some exciting stuff. We had students do a walk on the number line. (Start, turn, walk, stop) and then we wrote it down. 5 + -4 = 1. We discussed how non-threatening it was to walk for something like this, and it was a place where you were really free to experiment. When someone brought up different options, 7 - 13 or 7 + -13, we talked about how you can tell and was there really a difference. Then we hit on the idea that you could walk out equivalences. Are these two things equal? Let's try them! Someone had the idea to try commutativity. What would associativity look like? (Hard to walk.) There was an interesting side effect: some common student errors are impossible to walk. They just don't make sense in embodied cognition land

I brought a game idea, of course. Take a deck of cards, remove everything but A to 7, red is negative and black is positive.

End of the Line (game)
Shuffle, and deal two decks, like for War. Both players start at zero, facing each other. Flip the top card of your deck. Player with the smaller magnitude number goes first. You can add your number to yourself or subtract it from your opponent. The first player's move decides whether they are going positive or negative, and the 2nd player is going the other way. The goal is to get off the number line. (Ours went to +15 and -15.)

Sample turn:

player Positive is at 2 and flips red 6. Negative is at -3 and flips red 2.

Smaller magnitude goes first, so Negative adds -2 to their position.

Faces positive and walks back two squares to -5. Positive player doesn't want to add -6, so makes Negative subtract. Negative faces negative, then walks backward 6 squares to 1.

In the picture there are two different games going on. Other students tried the game or modeling stories with a chip model. People liked the game pretty well with the numberline, and got them a lot of practice thinking about adding and subtracting positive and negative, as well as use on the numberline.

Day 3 involved no embodied cognition. We discussed fact families and addition and subtraction strategies, and then discussed how to show a variety of strategies for integer addition and subtraction in symbolic records and in number lines. The number lines really showed the benefit of the previous classes' movement as they felt the directions really made sense.

All in all, great start to the year. I've only become more convinced of the need for more opportunities to embody mathematics, and the value of the intuition that this helps build through experience. And, of course, I'm interested in your stories about this, or ideas for what else you might have tried.

EDIT/postscript: several of the preservice teachers are blogging about this.

BlogCatalog

MathBlogs.com

My blog has recently been added to Math Blogs, which is part of one of the largest networks of blog directories on the Web. Please visit my blog's personal page to vote for my blog and comment to other blog users.